About

Assessment for Learning: Resources for First Year Undergraduate Mathematics Modules

Overview of the project:

This project concerns the development of formative assessment techniques and resources in order to improve the teaching and learning experience of first year undergraduate mathematics modules. Black and Wiliam (1998) defined formative assessment as ‘encompassing all those activities undertaken by teachers, and/or by their students, which provide information to be used as feedback to modify the teaching and learning activities in which they are engaged’ (p7-8). The work in our project has two main components: firstly we have created formative assessment tools for use in the classroom; secondly, we have developed interactive tasks which can be used by students to monitor their own progress and we are supporting this progress with the provision of online resources.

We have developed an audience response system UniDoodle which consists of lecturer and student apps for both android and ios systems. Students can submit graphs, drawings, text and calculations, and lecturers can view the responses instantly.

We have conducted a survey of lecturers in Mathematics and Engineering Departments in all Higher Education Institutions (HEIs) in Ireland and students in the partner institutions to ascertain the main topics and concepts that students find difficult in first year courses, the types of resources that are already in use in relation to these topics, and how they are disseminated. We found that the most problematic topics identified by students were integration, differentiation, functions, logarithms and limits. In contrast, lecturers were most concerned about students’ lack of ability in some basic algebra such as formula manipulation, solving equations and fractions. Lecturers stated that many of the problems students have with more advanced topics are related to a lack of these basic skills. When asked about types of resources, students requested more worked examples, step-by-step solutions and real-world examples. Lecturers preferred the idea of interactive resources that allow students develop conceptual understanding and examples that are contextualised.

A range of resources on the topics identified above:

An inventory of useful existing resources;

Moodle Courses and assessments using Khan Academy materials;

Online ‘lessons’ and quizzes designed in Moodle;

Student screencast continuous assessment projects;

Matlab practicals involving ‘real-world’ problems;

A suite of interactive tasks.

An evaluation of the effectiveness of these resources. We have conducted trials of all resources developed in this project. The resources have been modified as necessary based on the results of these trials and consultations with staff members and students. We have seen that our resources can be used to increase student engagement and develop conceptual understanding. We will continue to publish research articles on this evaluation.

We will conduct trials of all resources developed in this project over the next 12 months in appropriate mathematics modules at the partner institutions. The resources will be modified as necessary based on the results of these trials and consultations with staff members and students.

Benefits to the National Higher Education Sector:

The data we have gathered on the troublesome concepts in first year will be useful when lecturers are designing first year undergraduate mathematics courses and resources.

The audience response app will be freely available and will be useful in many situations, especially in STEM classrooms.

All resources will be made available to the whole higher education community via a dedicated website.

The research carried out in this project will add to the body of knowledge on education at tertiary level.

Benefits to Students:

Many of the resources developed from this project are targeted at the problem areas that students’ themselves have identified.

The resources will shortly be readily available to students and aim to provide opportunities for students to develop their conceptual understanding of ‘troublesome’ concepts. Some of the resources are adaptive in nature, providing individualised support to students.

The project has explored ways of using formative assessment to present students with opportunities to learn in new ways and to maximise student engagement. For example, using the audience response system to allow students and lecturers gain information about levels of understanding in classtime, asking students to create screencasts to explain troublesome topics, using interactive tasks to ask students to experiment and make conjectures.

Other national/international work that complements this project:

National Forum for the Enhancement of Teaching and Learning funded project ‘Transitioning to e-assessment in mathematics education’ based in UCC and CIT.

Improving progress for lower achievers through formative assessment in mathematics and Science (Fasmed). This an EU FP7 project based at the University of Newcastle. The Irish partner institution is Maynooth University.

Task design projects – most of these projects have been concerned with school-level mathematics. For example, Professor Malcolm Swan and his team at the University of Nottingham have been working on designing tasks for secondary school syllabi for many years. See http://map.mathshell.org/.